Anomalies and gauging of U(1) symmetries

Abstract

We propose the Symmetry TFT for theories with a $U(1)$ symmetry in arbitrary dimension. The Symmetry TFT describes the structure of the symmetry, its anomalies, and the possible topological manipulations. It is constructed as a BF theory of gauge fields for groups $U(1)$ and $\mathbb{R}$, and contains a continuum of topological operators. We also propose an operation that produces the Symmetry TFT for the theory obtained by dynamically gauging the $U(1)$ symmetry. We discuss many examples. As an interesting outcome, we obtain the Symmetry TFT for the non-invertible $\mathbb{Q}/\mathbb{Z}$ chiral symmetry in four dimensions.

Two columns, 12 pages. v2: refs added, more clear exposition. v3: refs added, typos corrected. v4: discussion added to sec. 3.A, matches published version

References in corpus (16)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Higher Gauging and Non-invertible Condensation Defects
• Orbifold groupoids
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Universal Non-Invertible Symmetries
• Non-Invertible Symmetries from Holography and Branes
• Unifying Constructions of Non-Invertible Symmetries
• Non-Invertible Defects in 5d, Boundaries and Holography
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Anomalous Symmetries End at the Boundary
• On the Symmetry TFT of Yang-Mills-Chern-Simons theory
• The algebra of anomaly interplay
• Holographic duals of symmetry broken phases
• (3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases

Cited by in corpus (14)

• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• Duality via Sequential Quantum Circuit in the Topological Holography Formalism
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• Non-Invertible $SO(2)$ Symmetry of 4d Maxwell from Continuous Gaugings
• (-1)-Form Symmetries and Anomaly Shifting from SymTFT
• Generalized Landau Paradigm for quantum phases and phase transitions
• Diagrammatics, Pentagon Equations, and Hexagon Equations of Topological Orders with Loop- and Membrane-like Excitations
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• $N$-ality symmetry and SPT phases in (1+1)d
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory